Four lectures on strongly coupled Quark Gluon Plasma

The four lectures are divided evenly between phenomenology and theory. Lecture 1 describes the hydrodynamical treatment of the high energy heavy ion collisions: we discuss in it the appearance of the notion of the "strongly coupled" QGP. Another phenomenological lecture is about perturbations of this expansion, by fluctuations of different types. We will in particularly argue that matter in a near-T_c situation is quite special, with an electric field imbedded in it for a long time: this situation should be described by dual-magnetohydrodynamics (DMHD). Two theoretical lectures focus on two dualities. The electric-magnetic duality, describing gradual transition from electric plasma at high-T to a magnetic-dominated plasma in the near-T_c domain. The last lecture is about applications of AdS/CFT duality, between strongly coupled N = 4 SYM gauge theory in 4 dimensions and string theory in the A d S₅ * S⁵ background.